Another spectacular closing ceremony last night brought London 2012 to a close, with Paralympians gathered in the same stadium that so recently hosted their Olympian colleagues. And it is that spirit of shared endeavour which brings home more powerfully than words how far these Games have changed perceptions of disability forever. This is something I feel strongly about because my mother was a wheelchair user. She was diagnosed with multiple sclerosis before I was born and such was the prevailing attitude 50 years ago that her doctors told her she was mad even to think of having a child. “You won’t be able to look after him,” her own mother counselled her. This concern turned out to be misplaced; but my mother’s task wasn’t made any easier by the reaction we met whenever we went out, a mixture of curiosity, prejudice and stigmatising. Her defiant response, and the constant retort of my childhood, was to insist that we were “normal”.

It became a kind of mantra in our house, a way to deflect the taunts at school (“why is your mum a spaz?”) and the looks of pity when we were out and about (“poor old soul,” I heard the mother of a classmate remark as she watched us walk away from the school gates with me pushing the wheelchair). That word “normal”, unfashionable in our more PC days (how would we cope now with another adjective of my childhood “invalid”, literally in-valid?) has been echoing in my ears as I have watched Paralympians run, jump, swim and ride higher, further, faster, better. Their achievements are, of course, so much more than “normal”, in sporting terms, but it has been the sight of them doing it so magnificently, watched by the world, that has dissolved those artificial barriers between non-disabled and disabled that blighted my childhood.

Legacy has been a big theme of London 2012: with luck, this well-run global spectacle will help regenerate east London, boost our flat-lining economy and leave a sense of rekindled national pride. But I hope it also banishes forever the sort of unthinking attitudes that regard people with disabilities as different and inferior. We can, after all, pass as many anti-discrimination laws as you like; but until we tackle the unspoken prejudices that mean employers still instinctively chose the candidate who can walk rather than the one who can’t for the job vacancy, there is still a long way to go. Though, thanks to the Paralympics, not so far now.

Anyone on an interview board who has marvelled at the stamina, skill and strength of Ellie Simmonds, Oscar Pistorius, Jonnie Peacock, Jason Smyth and so many others will hopefully think twice before they dismiss the “disabled candidate” for the post. Or even think of them in those terms. And those who sniggered along with the loathsome Little Britain sketch of Andy, the wheelchair user who is only pretending so he can scrounge off the rest of us, should now blush at the memory of their laughter.

So, what are the next steps? In the run-up to the Games, much pride was taken in the Olympics coming back to Britain for the third time. But 2012 was also a coming home for the Paralympics. They began, in modest circumstances, just after the Second World War at Stoke Mandeville Hospital in Buckinghamshire, where Ludwig Guttmann decided that the patients with spinal cord injuries he was treating could benefit from participation in competitive sport. It was a question of what they could do following their injury, he insisted, not what they couldn’t.

His vision took to the international stage in 1960 in Rome with what became the first Paralympic Games. Back then only a tiny number of countries participated. Today, the reach is almost universal. Tanni Grey-Thompson, one of Britain’s greatest Paralympians, has drawn particular attention to the success of the Chinese team, and has spoken of how official determination to do well has revolutionised attitudes to disability in Chinese society. Until recently babies born with disabilities were left outside orphanages or on doorsteps to die. Today, there is a programme of support. Sport can precipitate wider change.

However, some of the nations at the top of the Paralympic medals table do come as something of a surprise. When you have grown up pushing your mother in a wheelchair, your eyes are forever attuned to the presence of drop-kerbs, ramped access, accessible loos and the infrastructure required to make equality more than fine words. In southern Europe, these are all few and far between. In Brazil, home to the blade runner Alan Oliveira, I saw not one. China and Russia, who outpaced us in the medals’ table, also lag a long way behind Britain, the United States and Canada with such provision. So we must not get carried away with the notion that consigning disabled people to a ghetto is now a thing of the past.

And that is true even in this country. How many MPs are wheelchair users? A random measurement, perhaps, but a symbolic one. An estimated one in nine people have some form of disability, but only one member of the Commons, Dame Anne Begg, uses a wheelchair. That is not because the Palace of Westminster is inaccessible – though it could do better – but because selection committees in the constituencies are still just as hidebound as employers by outdated notions.

Where sport has led this past fortnight, others must follow. Not every person with a disability has the desire or the skill to compete in the Paralympics. My mother’s ambitions were more modest – home, parenthood and, if possible a career. This last goal proved impossible. Even though her gnarled fingers could type like fury, no one ever wanted her in their office.

And talk of ghettos brings us on to what is perhaps the most sensitive question about the Paralympics – the fact that the events all take place separately from the Olympics. The determination of Oscar Pistorius to compete on equal terms with non-disabled competitors was a hugely powerful message. He showed that there is an appetite to blur these boundaries. The practical obstacles are immense, and in some areas of competition they are insurmountable, but not always.

Take the example of CandoCo, an integrated dance company which took part in the closing ceremony. It was set up 20 years ago by two dancers – Adam Benjamin, who is able-bodied, and Celeste Dandeker, who sustained a spinal cord injury while performing on stage with London Contemporary Dance. Their vision, which many in the dance world doubted at the time, was to create a company where all that mattered was ability and the highest standards of creativity.

Two decades on and CandoCo has worked with all the great contemporary choreographers. Indeed they queue up for the chance. The company performs around the globe and wins plaudits and awards by the lorry-load. But the most inspiring thing – at least to someone who grew up wishing that people would stop noticing his mother’s wheelchair and instead see the person sitting in it – is that when you attend a CandoCo performance it is irrelevant which dancers are disabled and which non-disabled. Those barriers that society erects, wittingly or not, just disappear. So much so that, in fact, that no one would think of asking the performers the sort of questions that, I’m afraid, occasionally slipped out of TV reporters’ lips when greeting Paralympic medal winners, namely “and what exactly is wrong with you?” if not exactly those words.

There is, in other words, a lot further to travel, but we are already getting there in the arts. Another dazzling feature of the closing ceremony was the Paraorchestra which played alongside Coldplay as the flag was lowered. Its conductor, Charles Hazlewood, wants to ease the passage of many more disabled musicians into mainstream orchestras, from which they are almost absent.

Music, Hazlewood points out, is a universal language that makes no distinction over who can walk or see. Dance, as CandoCo demonstrates so powerfully, is open to all-comers. And sport, in the wake of the Paralympics, can now boast the same. That can have a transformative effect on all our lives.

Peter Stanford was chairman for 20 years of Aspire, the national spinal injuries charity